Reasoning with Forest Logic Programs and f-hybrid Knowledge Bases

Open Answer Set Programming (OASP) is an undecidable framework for integrating ontologies and rules. Although several decidable fragments of OASP have been identified, few reasoning procedures exist. In this article, we provide a sound, complete, and terminating algorithm for satisfiability checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules have a tree shape and allow for inequality atoms and constants. The algorithm establishes a decidability result for FoLPs. Although believed to be decidable, so far only the decidability for two small subsets of FoLPs, local FoLPs and acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a hybrid framework where \SHOQ{} knowledge bases and forest logic programs co-exist, and we show that reasoning with such knowledge bases can be reduced to reasoning with forest logic programs only. We note that f-hybrid knowledge bases do not require the usual (weakly) DL-safety of the rule component, providing thus a genuine alternative approach to current integration approaches of ontologies and rules

Towards Closed World Reasoning in Dynamic Open Worlds (Extended Version)

The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge bases composed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve. In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties. To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.Comment: 40 pages; an extended version of the article published in Theory and Practice of Logic Programming, 10 (4-6): 547 - 564, July. Copyright 2010 Cambridge University Pres

Paraconsistency in hybrid logic

As in standard knowledge bases, hybrid knowledge bases (i.e. sets of information specified by hybrid formulas) may contain inconsistencies arising from different sources, namely from the many mechanisms used to collect relevant information. Being a fact, rather than a queer anomaly, inconsistency also needs to be addressed in the context of hybrid logic applications. This article introduces a paraconsistent version of hybrid logic which is able to accommodate inconsistencies at local points without implying global failure. A main feature of the resulting logic, crucial to our approach, is the fact that every hybrid formula has an equivalent formula in negation normal form. The article also provides a measure to quantify the inconsistency of a hybrid knowledge base, useful as a possible basis for comparing knowledge bases. Finally, the concepts of extrinsic and intrinsic inconsistency of a theory are discussed

A semantical framework for hybrid knowledge bases

In the ongoing discussion about combining rules and ontologies on the Semantic Web a recurring issue is how to combine first-order classical logic with nonmonotonic rule languages. Whereas several modular approaches to define a combined semantics for such hybrid knowledge bases focus mainly on decidability issues, we tackle the matter from a more general point of view. In this paper, we show how Quantified Equilibrium Logic (QEL) can function as a unified framework which embraces classical logic as well as disjunctive logic programs under the (open) answer set semantics. In the proposed variant of QEL, we relax the unique names assumption, which was present in earlier versions of QEL. Moreover, we show that this framework elegantly captures the existing modular approaches for hybrid knowledge bases in a unified way

A Goal-Directed Implementation of Query Answering for Hybrid MKNF Knowledge Bases

Ontologies and rules are usually loosely coupled in knowledge representation formalisms. In fact, ontologies use open-world reasoning while the leading semantics for rules use non-monotonic, closed-world reasoning. One exception is the tightly-coupled framework of Minimal Knowledge and Negation as Failure (MKNF), which allows statements about individuals to be jointly derived via entailment from an ontology and inferences from rules. Nonetheless, the practical usefulness of MKNF has not always been clear, although recent work has formalized a general resolution-based method for querying MKNF when rules are taken to have the well-founded semantics, and the ontology is modeled by a general oracle. That work leaves open what algorithms should be used to relate the entailments of the ontology and the inferences of rules. In this paper we provide such algorithms, and describe the implementation of a query-driven system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic) rules under the well-founded semantics and a (monotonic) ontology, represented by a CDF Type-1 (ALQ) theory. To appear in Theory and Practice of Logic Programming (TPLP

Reasoning with Inconsistencies in Hybrid MKNF Knowledge Bases

This article is concerned with the handling of inconsistencies occurring in the combination of description logics and rules, especially in hybrid MKNF knowledge bases. More precisely, we present a paraconsistent semantics for hybrid MKNF knowledge bases (called para-MKNF knowledge bases) based on four-valued logic as proposed by Belnap. We also reduce this paraconsistent semantics to the stable model semantics via a linear transformation operator, which shows the relationship between the two semantics and indicates that the data complexity in our paradigm is not higher than that of classical reasoning. Moreover, we provide fixpoint operators to compute paraconsistent MKNF models, each suitable to different kinds of rules. At last we present the data complexity of instance checking in different para-MKNF knowledge bases